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Black_prince [1.1K]
3 years ago
15

Find all the zeros of the function g(x)=x^3-4x^2-x+22

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
5 0

Answer:

x = -2, x = 3 − i√8, and x = 3 + i√8

Step-by-step explanation:

g(x) = x³ − 4x² − x + 22

This is a cubic equation, so it must have either 1 or 3 real roots.

Using rational root theorem, we can check if any of those real roots are rational.  Possible rational roots are ±1, ±2, ±11, and ±22.

g(-1) = 18

g(1) = 18

g(-2) = 0

g(2) = 12

g(-11) = 1782

g(11) = 858

g(-22) = -12540

g(22) = 8712

We know -2 is a root.  The other two roots are irrational.  To find them, we must find the other factor of g(x).  We can do this using long division, or we can factor using grouping.

g(x) = x³ − 4x² − 12x + 11x + 22

g(x) = x (x² − 4x − 12) + 11 (x + 2)

g(x) = x (x − 6) (x + 2) + 11 (x + 2)

g(x) = (x (x − 6) + 11) (x + 2)

g(x) = (x² − 6x + 11) (x + 2)

x² − 6x + 11 = 0

Quadratic formula:

x = [ 6 ± √(36 − 4(1)(11)) ] / 2

x = (6 ± 2i√8) / 2

x = 3 ± i√8

The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.

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A flood a creek's water level changes by −4 7/10 feet in 2 hours. What is the average change in the creek's water level per hour
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2 years ago
In ΔMNO, m = 780 inches, o = 760 inches and ∠O=164°. Find all possible values of ∠M, to the nearest degree.
Mademuasel [1]

Answer:

So the answer is both

180 and 328 (but it may or may not show you "not possible, if so, then you got it right)

Step-by-step explanation:

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1. SinM/780 = Sin164/760

2. 780sin164/760 = 0.2828909704

3. M = sin^-1 (0.2828909704)= 16.4328229 or 16

Check for possibility

180-16= 164

164 + 16= 180 (not possible)

164 + 164= 328 (not possible)

4 0
2 years ago
Read 2 more answers
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